Evaluate 5^(3/4)*5^(3/8)

$5^{\frac{3}{4}} \cdot 5^{\frac{3}{8}}$

Step 1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5^{\frac{3}{4} + \frac{3}{8}}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5^{\frac{3}{4} \cdot \frac{2}{2} + \frac{3}{8}}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$5^{\frac{3 \cdot 2}{4 \cdot 2} + \frac{3}{8}}$

Multiply $4$ by $2$ .

$5^{\frac{3 \cdot 2}{8} + \frac{3}{8}}$

Step 4

Combine the numerators over the common denominator.

$5^{\frac{3 \cdot 2 + 3}{8}}$

Step 5

Simplify the numerator.

Multiply $3$ by $2$ .

$5^{\frac{6 + 3}{8}}$

Add $6$ and $3$ .

$5^{\frac{9}{8}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$5^{\frac{9}{8}}$

Decimal Form:

$6.11422272 \dots$